Exile is a card name I thought we'd see in Nocturne back when it came out. It sounds like it fits the theme to me.
Not sure the "if you did" is necessary... I don't even think there's a possible way to play the card and not end up following the first instruction. You'll always have at least 1 card in play or in hand.
And even though the challenge rules specified Island Mat as a mechanic; I think it would be better without it... the Island Mat doesn't mean anything; it has no rules associated. It's as arbitrary as putting in on your Tavern Mat, or a new Exile Mat, or just setting it aside forever. And very similar to trashing it.
Since the Island mat already exists that seemed easier than making a new mat and better than just saying "set a card aside somewhere". Besides, Island fits thematically. I don't really care where the card goes. Whether it says put the card on your island or put the card in your pocket, I don't really care. Island seems fine to me though.
Fortunately, even if I did get rid of the Island part, it is a Night and it has Villagers, so it still fits the challenge
As for the if you did part, yeah you're right, it can probably be left off.
I just like the feeling of "do A for B" rather than two unrelated effects. Maybe I should just word it like ".... your Island mat
for +1 Coffers or +1 Villager"